Granular-ball Guided Masking (GBGM)

• GBGM is a structure-aware data augmentation technique that leverages granular-ball computing to generate adaptive binary masks by preserving semantically informative regions.
• It employs a hierarchical, coarse-to-fine masking mechanism to selectively retain key image structures while suppressing redundant areas, thereby boosting model robustness.
• GBGM integrates seamlessly into deep learning workflows without altering network architectures, consistently improving classification and masked image reconstruction tasks.

Granular-ball Guided Masking (GBGM) is a structure-aware data augmentation technique that leverages Granular-ball Computing (GBC) to generate adaptive binary masks for image-level or feature-level regularization in deep neural networks. GBGM integrates a hierarchical, coarse-to-fine masking mechanism that selectively preserves semantically informative and structurally significant regions of input data, while suppressing redundant or homogeneous areas. This approach is applied in a model-agnostic fashion during training and enhances the robustness and generalization capability of CNNs and Vision Transformers by constraining the model to exploit complementary visual cues. GBGM demonstrates consistent improvements in supervised classification and masked image reconstruction tasks across various datasets and architectures (Xia et al., 24 Dec 2025).

1. Granular-ball Computing: Theoretical Framework

Granular-ball Computing (GBC) provides the foundation for structure-aware masking. In GBC, a granular-ball $\mathcal{GB}_j$ is defined as a compact set of pixels or feature vectors:

$\mathcal{GB}_j = \{y_i \mid i=1, \ldots, m_j\}$

where $m_j$ is the cardinality of the set. The center $c_j$ and radius $r_j$ of a granular-ball are given by:

$$c_j = \frac{1}{m_j}\sum_{i=1}^{m_j} y_i\,, \qquad r_j = \frac{1}{m_j}\sum_{i=1}^{m_j} \lVert y_i - c_j \rVert$$

Purity, defined as the radius $r_j$, quantifies the homogeneity of each region; smaller radii correspond to more coherent balls.

The splitting criterion employs the $L_2$ distance,

$d(y_i, y_k) = \lVert y_i - y_k \rVert_2\,,$

and iteratively divides any granular-ball with $r_j > T$ (for some threshold $T$) into smaller balls until $r_j \le T$ for all. This process constructs a multi-scale spatial hierarchy, with coarse granular-balls corresponding to large homogeneous image regions (e.g., background) and fine granular-balls to local details and object boundaries.

2. GBGM Algorithm: Multi-Stage Structure-Aware Masking

GBGM generates structure-aware binary masks through a three-stage process:

• Stage 1: Coarse Granularity Masking The image $X \in \mathbb{R}^{H \times W \times 3}$ is partitioned into a regular grid of blocks of size $S_1 \times S_1$. For each block $\mathcal{P}_{i,j}$, a purity score is computed via the average deviation from its mean intensity:

$$\mathrm{Purity}(\mathcal{P}_{i,j}) = \frac{1}{|\mathcal{C}|}\sum_{(u,v)\in\mathcal{C}} \big| \mathcal{P}_{i,j}(u,v) - \mu(\mathcal{P}_{i,j}) \big|$$

High-purity blocks represent informative structures and are retained; others are candidates for further refinement.

• Stage 2: Finer Granularity Masking Blocks rejected in Stage 1 are subdivided into smaller sub-blocks ($2 \times 2$, size $S_2 = S_1/2$). Purity scores are recomputed for these finer blocks, and the top-k are preserved.
• Stage 3: Importance Mask Generation The binary mask from Stage 2 is convolved with a $3 \times 3$ all-ones kernel to assess the local density of informative regions, normalized to $[0,1]$, and combined with randomized thresholding to induce spatial diversity. The resulting low-resolution mask is upsampled to the original image size.

The overall masking preserves spatially coherent, high-information regions (object bodies, edges) and stochastically suppresses large homogeneous areas. This hierarchy ensures the retention of both global context and fine-grained local semantically salient features.

3. Practical Integration into Deep Learning Workflows

GBGM is applied dynamically on each training iteration. For every input image, the computed binary mask $\mathcal{M}_\mathrm{final}$ is used for element-wise masking:

$X' = X \odot \mathcal{M}_\mathrm{final}$

This process does not require any modification to the network architectures (ResNet, EfficientNet, ViT, Swin, etc.) or objectives, thus maintaining pipeline compatibility.

For masked autoencoder (MAE) frameworks, GBGM replaces conventional random patch masking, resulting in more semantically meaningful masked image modeling. The approach is entirely label-free and model-agnostic.

4. Hyperparameters and Implementation Considerations

GBGM parameters are dataset-dependent:

Dataset	Coarse Block Size $S_1$	Grid Size	Fine Block Size $S_2$	Typical Mask Ratio
CIFAR-10/100	4	$8 \times 8$	—	10–20%
ImageNet	$\approx$32	$7 \times 7$	16	10–20%

Mask-out ratios of 10–20% provide effective regularization without excessive semantic loss. The random thresholding constant $\varepsilon$ (typically $10^{-6}$) ensures numerical stability. Mask intensity may be scheduled per epoch or annealed. GBGM entails $O(HW)$ computational complexity and practical inference overheads of $\sim$3.8 ms per $224\times224$ image.

5. Empirical Evaluation and Comparative Analysis

Classification

GBGM consistently yields statistically significant improvements:

• CIFAR-10 (ResNet-44): Baseline 93.10%, GBGM 94.68% (+1.58%), random masking 91.29%.
• CIFAR-100 (EfficientNet-L2+SAM): Baseline Top-1 94.79%, GBGM Top-1 94.95%; Top-5 from 99.30% to 99.45%.
• ImageNet-1K: EfficientNet-B0 Top-1 from 74.31% to 74.68%; Swin-Tiny from 80.31% to 80.78%.

Masked Image Reconstruction

For MAE reconstruction on ImageNet-100:

• PSNR: Improvements from 8.22 dB (MAE) to 8.26 dB (MAE+GBGM)
• SSIM: From 0.231 to 0.252
• LPIPS: From 0.640 to 0.623

Qualitative outputs show sharper contours and enhanced textural fidelity in masked image reconstructions.

Ablation

• 10% mask ratio optimizes regularization vs. information preservation; 20% marginally worse.
• Two-stage masking outperforms single-stage on higher-resolution datasets, particularly for small object features.
• Purity-guided masking consistently outperforms random masking for a fixed deletion ratio.

6. Methodological Significance and Future Directions

GBGM synthesizes the spatial adaptivity of granular-ball computing with explicit structure-aware augmentation, resulting in masks tailored to image semantics. A salient feature is its hierarchical, multigranular selection, which maintains global and local context, maximizing the effectiveness of data augmentation relative to random or purely spatial partition-based methods.

The method is computationally lightweight, requires no architectural modifications, and generalizes across dataset scales and network backbones. A plausible implication is that extending GBGM to dynamically adjust mask ratios according to image complexity, or employing it in dense prediction paradigms (segmentation, detection), could further enhance its effectiveness. Application to spatio-temporal domains (e.g., video) presents a natural direction for future research (Xia et al., 24 Dec 2025).